Question

Rectangle PQRS is graphed in the coordinate plane.

Part A


Rectangle PQRS is rotated 90°

counterclockwise about the origin to create rectangle P'Q'R'S' (not shown). What are the coordinates of point R'?


Responses


(−7,6)


(7,6)


(−6,7)


(6,7)


Question 2


Part B


Rectangle PQRS is reflected across the y-axis and then translated down 2 units to create rectangle P''Q''R''S'' (not shown). What are the coordinates of Q''?

Responses


(−6,0)


(6,0)


(−6,−4)


(−6,2)

THE ANSWERS THAT ARE YELLOW IN THE PICTURE ARE WRONG DONT PICK THEM

Answer 1

Part A: (b) (7, 6)

Part B: (c) (-6, -4)

Explanation:

You want the coordinates of points of rectangle PQRS that have been subject to rotation, reflection, and translation.

A. Rotation

Rotation 90° CCW is accomplished by the transformation ...

(x, y) ⇒ (-y, x)

Then point R gets rotated to ...

R(6, -7) ⇒ R'(7, 6)

B. Reflection, translation

Reflection across the y-axis changes the sign of the x-coordinate:

(x, y) ⇒ (-x, y) . . . . . . reflection in the y-axis

Translation adds the translation amount to the relevant coordinate:

(x, y) ⇒ (x, y -2) . . . . translation down 2 units

Together, the effect on point Q is ...

(x, y) ⇒ (-x, y -2)

Q(6, -2) ⇒ Q''(-6, -4)

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Additional comment

You can figure the transformation related to rotation by considering "where did it come from?"

If a point ends up on the x-axis after a rotation of 90° CCW, it had to come from the -y axis.

If a point ends up on the y-axis after a rotation of 90° CCW, it had to come from the +x axis.

These observations can be written as the transformation ...

(x, y) ⇒ (from -y, from +x) = (-y, x) . . . . . . rotation 90° CCW

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